Thinking Mathematically (6th Edition)

Published by Pearson

Chapter 2 - Set Theory - 2.2 Subsets - Exercise Set 2.2: 67

Answer

The total number of proper subsets is $7$.

Work Step by Step

Represented with the roster method, the set looks like this: $\{3, 4, 5\}$ A set of $n$ elements has $2^n$ subsets. This set has 3 elements; therefore, it has $2^3=8$ subsets. However, we are asked for distinct subsets, so we have to take 1 from the result, as one of the subsets is going to be the set itself. The total number of proper subsets is $8-1=7$.

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